The object of this paper is to study the relationship between certain projective modules and
their endomorphism rings. Specifically, the basic problem is to describe the projective …

Mares [9] has called a projective module semiperfect if every homomorphic image has a
projective cover and has shown that many of the properties of semiperfect rings can be …

In analogy to the elementwise definition of von Neumann regular rings an $ R $-module $ M
$ is called regular if given any element $ m\in M $ there exists $ f\in {\operatorname {Hom} …

This paper is a loosely connected collection of results on rings and modules. The first
section is concerned with quasi-injective modules of a ring. A module M is said to be quasi …

Let R be an integral domain in which all finitely generated ideals are principal. Let M be a
projective R-module. It is well known that if M is finitely generated it is free. By a familiar …

Let I be an ideal of a ring R. Consider the following conditions on R: 1. If X is a finitely
generated submodule of a finitely generated projective module P, then X= A⨁ B where is a …

1. Introduction, In this paper we prove several theorems about rings having a generous
supply of projective injective modules. This is a curious class of rings. For instance, every …

Introduction. The aim of this paper is to study conditions which reflect the projectivity of a
given finitely generated flat module over a commutative ring. The use of the invariant factors …

One of the aims of this paper is to answer the following question: Let A be a commutative
ring for which projective ideals are finitely generated; is the same valid in A [x], the …

A module is serial if its submodules are linearly ordered with respect to inclusion. A ring R is
called left serial if RR is a direct sum of serial modules, and R is called serial if it is both left …